Overview

This work deals with linear functional differential equations and operator theory methods for their investigation. The main topics are: the equivalence of the input-output stability of the equation x = and the invertibility of the operator in the class of casual operators; the equivalence of input-output and exponential stability; the equivalence of the dichotomy of solutions for the homogeneous equation x = 0 and the invertibility of the operator; the properties of Green's function; the independence of the stability of an equation from the norm on the space of solutions; shift invariant functional differential equations in Banach space; the possibility of the reduction of an equation of neutral type to an equation of retarded type; special full subalgebras of integral and difference operators, and operators with unbounded memory; and the analogue of Fredholm's alternative for operators with almost periodic coefficients where one-sided invertibility implies two-sided invertibility.

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U.G. Kurbatov Functional Differential Operators and Equations This book provides a thorough and rigorous presentation of the use of operator theory methods to study the linear theory of functional-differential equations ... It is a practically self-contained book by means of which students and researchers working in functional analysis can be introduced to the abstract linear theory of functional-differential equations. --MATHEMATICAL REVIEWS

U.G. Kurbatov <p>Functional Differential Operators and Equations <p> This book provides a thorough and rigorous presentation of the use of operator theory methods to study the linear theory of functional-differential equations . . . It is a practically self-contained book by means of which students and researchers working in functional analysis can be introduced to the abstract linear theory of functional-differential equations. a MATHEMATICAL REVIEWS

U.G. Kurbatov Functional Differential Operators and Equations This book provides a thorough and rigorous presentation of the use of operator theory methods to study the linear theory of functional-differential equations ... It is a practically self-contained book by means of which students and researchers working in functional analysis can be introduced to the abstract linear theory of functional-differential equations. -MATHEMATICAL REVIEWS

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